Marketing companies are interested in knowing the population percent of women who make the majority of household purchasing decisions.

a) When designing a study to determine this population proportion, what is the minimum number you would need to survey to be 90% confident that the population proportion is estimated to within 0.05? (Round your answer up to the nearest whole number.)

b) Suppose a marketing company did do a survey. They randomly surveyed 200 households and found that in 120 of them, the woman made the majority of the purchasing decisions. We are interested in the population proportion of households where women make the majority of the purchasing decisions.
Identify the following. (Enter exact numbers as integers, fractions, or decimals.)

1) x

2) n

3) p'

In a multiple linear regression with 40 observations, the following sample regression equation is obtained:

yˆy^ = 12.5 + 2.4x₁ − 1.0x₂ with s_e = 5.41. Also, when x₁ equals 16 and x₂ equals 5, se(yˆ0)se(y^0) = 2.60.

[You may find it useful to reference the t table.]

a. Construct the 95% confidence interval for E(y) if x₁ equals 16 and x₂ equals 5. (Round intermediate calculations to at least 4 decimal places, "t_α/2,df" value to 3 decimal places, and final answers to 2 decimal places.)

b. Construct the 95% prediction interval for y if x₁ equals 16 and x₂ equals 5. (Round intermediate calculations to at least 4 decimal places, "t_α/2,df" value to 3 decimal places, and final answers to 2 decimal places.)

c. Which interval is wider?

• Confidence interval since it does not include the variability caused by the error term.

• Prediction interval since it includes the variability caused by the error term.

• Confidence interval since it includes the variability caused by the error term.

• Prediction interval since it does not include the variability caused by the error term.

2. Ogunmodede Medical Company stocks medical devices for hospitals in the state of Colorado. The average rate of demand for the prostheses is 100 per month and appears to be described quite well by a Normal distribution with standard deviation of 10. The procurement lead-time τ = 6 months. Each medical device costs $2,000. The cost of placing an order with the manufacturer, incoming inspection, etc. is estimated to be $100.00. The annual inventory carrying cost rate is 0.20. All stock outs are backordered. It is difficult to estimate the cost of being out of stock. Instead, it is required that the probability of being out of stock not be greater than 0.0005.

(a) If the facility is to operate as a [Q,r] system, determine Q∗ and r ∗ .

(b) What is the imputed cost of a backorder π?

(c) What is the cost of uncertainty?

Please ANSWER IN R CODE.

Problem:

Vital capacity is a measure of the amount of air that someone can exhale after taking a deep breath, Data was collected on brass players and a control group.

1. Put the data into a "long format" data frame. That is one column for vital measure and second character or factor column with the label of "Brass" or "Control".
2. Conduct a test using "t.test" to determine whether the population mean for brass is larger than that for control.
3. Provide the equivalent 95% confidence interval for the difference of two population means means.
4. A researcher claims that in theory the "spread/variance" in the two populations is the same. Repeat step 2 utilizing this assumption with the argument "var.equal"

Please provide all relevant work. That is your commands, the output and any interpretations/conclusions that are necessary.

In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of

69.6 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. a) Find a probability that a study participant has a height that is less than 66 inches. b) Find the probability that a study participant has a height that is between 66 and 72. c) Find the probability that a study participant has a height that is more than 72 inches. d)

inches.

On stat your assessment is based on: Final Exam 47% Learn based on‐line assessment 34% Assignments 19%

Consider three random variables X, Y and Z which respectively represent the exam, on‐line assessment total and assignment scores (out of 100%) of a randomly chosen student. Assume that X, Y and Z areindependent (this is clearly not true, but the answers may be a reasonable approximation).

Suppose that past experience suggests the following properties of these assessment items (each out of 100%): E(X) = 61, sd(X) = 20, E(Y) = 72, sd(Y) = 22 and E(Z) =65, sd(Z) = 24.

a) Find the distribution parameters, E(T) and Var(T), for the total mark, T, where:T = 0.47X+0.34Y+0.19Z.

b) Assume the on‐line assessment, exam and assignment scores are Normally distributed. If the pass mark is 50%, calculate the probability that a randomly selected student will pass.

c) Find the expected number of A+ grades (90% and above) to be awarded in July if there are 840 students on the course this semester.

d) If a random sample of 16 stat students is selected, what is the probability that their average grade is at least a B (that is, on average they get 70% or more in total)?

How are b, c and d answered using excel?

1. Noise pollution is measured in decibels. In California any motorcycle made after 1980 may not be any louder than 80 decibels. Harley Davidson claims their mean decibel rating on bikes is 70 with a variance of 10. The variance of the noise is questioned. Just because Harley has a mean that is less than 80, they could still be producing louder than acceptable bikes. The federal EPA conducts a sample of 30 bikes and determines the variance to be 20 decibels. Is there enough evidence to question Harley’s claim of 10 decibels?

(15pts)

1. Use the Hypothesis Test Method

1. Standard Normal Distribution P(z<c) = 0.7652 (two decimal places)

2. The mean score is 70, standard deviation is 11, P(x>c) = 0.44

3. Out of 100 people sampled, 61 had kids. Construct a 90% confidence interval for the true population proportion of people with kids. __<p<__ (three decimal places)

4. P(-0.88<z<0.4) (four decimal places)

5. Mean of 1500, standard deviation of 300. Estimating the average SAT score, limit the margin of error to 95% confidence interval to 25 points, how many students to sample?

6. Population proportion is 43%, would like to be 95% confident that your estimate is within 4.5% of the true population proportion. How large of a sample is required?

7. P(z<1.34) (four decimal places)

8. Candidate only wants a 2.5% margin error at a 97.5% confidence level, what size of sample is needed?

9. Estimate this proportion to within 4% at the 95% confidence level, how many randomly selected college students must we survey?

10. 420 people were asked if they like dogs, 22% said they did. Find the margin of error for the poll at 95% confidence level. (four decimals

1. Two cards are drawn from a deck of cards (consisting of 52 cards: 13 cards for each of the four suits, Spades (S), Hearts (H), Diamonds (D) and Clubs (C)). Drawing is done with replacement, that is, the first card is drawn, recorded and put back in the deck, then the second card is drawn and recorded. Assuming an outcome is recorded in the order which two cards are drawn, what is the sample space for this (random) phenomenon? Write all possible outcomes.

Assuming each card is likely to be drawn, and two draws are independent, what is the probability that two cards are of the same suit?(**) Write the last calculation formula and the final answer value.

3. We would like to know whether, on average, students learn better in a self-paced or in an instructor-paced computer learning environment. We randomly assigned 40 BL131 students to self-paced sessions and a different 40 students to an instructor-paced sessions for one unit and recorded the exam scores for that unit. The two-sided p-value for the comparison was 0.01. alpha = 0.05.

A) State your conclusion in context and say why you reached that conclusion.

We would like to know whether students learn better in a self-paced- or in an instructor-paced computer learning environment. We randomly assigned 40 BL131 students to self-paced sessions and a different 40 students to an instructor-paced sessions. Here are all the pieces of information from the analysis:

5. State the null and alternative hypothesis for this test.

6. Our test statistic is (xbar1-xbar2) but to actually get the critical values and p-values we use a t-ratio. What, in plain English, is the t-ratio telling us specifically? (And don’t say ‘whether to reject Ho)

In March 2014, Harris Interactive conducted a poll of a random sample of 2234 adult Americans 18 years of age or older and asked, "which is more annoying to you, tailgaters or slow drivers who stay in the passing lane?" Among those surveyed, 1184 were more annoyed by tailgaters

a) Explain why the variable of interest is qualitative with two possible outcomes. What are the two outcomes?

b) Verify the requirements for constructing a 90% confidence intervsl for the population proportion of all adult Americans who are more annoyed by tailgaters than slow drivers in the passing lane.

c)Construct a 90% confidence interval for the population proportion of all adult Americans who are more annoyed by tailgaters than slow drivers in the passing lane.

A statistics student wondered whether there might be a relationship between gender andcommuting methods among students at a high school. He surveyed 200 the high school students (92 males and 108 females) he happened to encounter around campus, asking each of them about their typical way of commuting to the college. The data from this survey appears below:

1. List the appropriate conditions for this test and explain why each has (or has not) been satisfied:

2. Compute the P-value for this test

3. State an appropriate conclusion for this test

A global research study found that the majority of today's working women would prefer a better work-life balance to an increased salary. One of the most important contributors to work-life balance identified by the survey was "flexibility," with 41% of women saying that having a flexible work schedule is either very important or extremely important to their career success. Suppose you select a sample of 100 working women.

The probability that in the sample fewer than 48​% say that having a flexible work schedule is either very important or extremely important to their career success is

The probability that in the sample between 33​% and 48​% say that having a flexible work schedule is either very important or extremely important to their career success is

The probability that in the sample more than 42% say that having a flexible work schedule is either very important or extremely important to their career success is

Based on the various stepwise approaches for selecting an excellent (if not optimal) fitted multiple regression model, which one approach would you select if you had to explain to a client what your chosen model is and what approach you used to obtain it?

The Wall Street Journal reported some interesting statistics on the job market. One statistic is that 40% of all workers say they would change jobs for "slightly higher pay." In addition, 88% of companies say that there is a shortage of qualified job candidates. Suppose 16 workers are randomly selected and asked if they would change jobs for "slightly higher pay."

Appendix A Statistical Tables

*(Round your answer to 3 decimal places when calculating using Table A.2.)
**(Round your answer to 4 decimal places.)
***(Round your answer to 1 decimal place.)

a. What is the probability that nine or more say yes? *
b. What is the probability that three, four, five, or six say yes? *
c. If 13 companies are contacted, what is the probability that exactly 10 say there is a shortage of qualified job candidates? **
d. If 13 companies are contacted, what is the probability that all of the companies say there is a shortage of qualified job candidates? **
e. If 13 companies are contacted, what is the expected number of companies that would say there is a shortage of qualified job candidates? ***